TABLE OF CONTENTS A waveguide is a guided wave structure formed from a single enclosed conductor. Figure 3.18 shows the most common type, the rectangular waveguide. When we solve the Helmholtz equation (2.34) for the electromagnetic field modes that can exist within the waveguide, we find that the TEM mode is not a solution [7]. Instead, an infinite number of transverse electric (TE) and transverse magnetic (TM) modes may exist. These modes have transverse components of the electric and magnetic fields. The TE modes also have a propagational ( z-directed) component of the magnetic field, and the TM modes have a propagational ( z-directed) component of the electric field. The dominant mode for standard sized rectangular waveguide having width a greater than height b is the TE 10 mode, which has the field components:
where ? 10 = [( ?/ a) 2? k 2] 1/2 is the propagation constant; Z TE 10 = jk ?/ ? 10 is the mode s wave impedance; and ? = ( ? 0 ? r / ? r ? 0) 1/2 is the intrinsic impedance of the dielectric filling the waveguide. The sinusoidal electric field profile is shown at the input to the waveguide in Figure 3.18. Propagation can occur only at frequencies greater than the cutoff frequency. The cutoff frequency for the TE 10 mode is the frequency at which ? 10 becomes equal to zero:
